feat(livestats): per-player killedBy + deathPosition + winner for live standings (#4593)

Enriches the admin-bot live-stats snapshot
(`/api/adminbot/game/:id/stats`) with the per-player fields a semi-live
standings board needs, so it can score kills + placement live instead of
waiting for the post-game record.

Per player in `liveStats.players[]`:
- **`killedBy`** — the eliminator's clientID (null while alive /
non-client killer). Invert → live kill points.
- **`deathPosition`** — finishing place at elimination = non-bot players
still standing + 1 (frozen at "last of the then-standing"). Null while
alive → live placement.

The **full roster** is reported (dead players are retained in the client
view), plus top-level **`winner`** (the decided winner's clientID, else
null).

Deterministic / consensus-safe: `killedBy` (stamped at `recordKill`) and
`deathPosition` (stamped in `PlayerExecution`) are pure sim values, so
in-sync clients agree on the majority vote; `winner` is added
server-side in `GameServer.liveStats()` from the winner vote (like the
existing publicID/username/connected enrichment).

- [x] I have added screenshots for all UI updates
- [x] I process any text displayed to the user through translateText()
and I've added it to the en.json file
- [x] I have added relevant tests to the test directory

tests/GameUpdateUtils.test.ts

@@ -18,6 +18,8 @@ function makePlayerState(overrides: Partial<PlayerState> = {}): PlayerState {
     smallID: 1,
     isAlive: true,
     isDisconnected: false,
+    killedBy: null,
+    deathPosition: null,
     tilesOwned: 0,
     gold: 0,
     troops: 100,
@@ -68,6 +70,14 @@ describe("diffPlayerUpdate", () => {
     expect(diff.hasSpawned).toBeUndefined();
   });
 
+  it("emits killedBy + deathPosition when a player is eliminated", () => {
+    const prev = makePlayerUpdate({ killedBy: null, deathPosition: null });
+    const next = makePlayerUpdate({ killedBy: "client-b", deathPosition: 3 });
+    const diff = diffPlayerUpdate(prev, next)!;
+    expect(diff.killedBy).toBe("client-b");
+    expect(diff.deathPosition).toBe(3);
+  });
+
   it("ignores tilesOwned/gold/troops — they travel via packedPlayerUpdates", () => {
     const prev = makePlayerUpdate({ gold: 100n, troops: 50, tilesOwned: 5 });
     const next = makePlayerUpdate({ gold: 200n, troops: 75, tilesOwned: 9 });
@@ -241,6 +251,16 @@ describe("packAttackTroopDeltas", () => {
 });
 
 describe("applyStateUpdate", () => {
+  it("applies killedBy + deathPosition on elimination", () => {
+    const target = makePlayerState();
+    applyStateUpdate(
+      target,
+      makePlayerUpdate({ killedBy: "client-b", deathPosition: 3 }),
+    );
+    expect(target.killedBy).toBe("client-b");
+    expect(target.deathPosition).toBe(3);
+  });
+
   it("applies every field from a full update", () => {
     const target = makePlayerState();
     const pu = makePlayerUpdate({